In this reporting period publications appeared in the following areas, listed in the same order as the accompanying references: 1. Single-molecule fluorescence spectroscopy; 2. Single-molecule force spectroscopy; 3. Kinetics in the presence of conformational fluctuations; 4. How the crowded environment in the cell affects reactions rates. These are discussed below in turn. The fifth paper on the list dealing with diffusion-influenced multisite phosphorylation was described in the last year report but actually appeared in print this year. Single-molecule Forster resonance energy transfer (FRET) between fluorescent donor and acceptor labels attached to a protein or nucleic acid is widely used to probe intramolecular distances and study the structure, dynamics and function of macromolecules. In these experiments, a molecule is either immobilized on a surface or diffuses through a spot illuminated by a laser, and the donor fluorophore is excited. The donor can emit a photon or transfer the excitation to an acceptor which then can emit a photon of a different color. The rate of transfer depends on the interdye distance and this is why there is information about conformational dynamics. The output of these experiments is a sequence of photons with recorded colors and arrival times. When a single molecule is excited by a pulsed laser, it is also possible to detect the time interval between the laser pulse and the photon. This so-called delay time is related to the fluorescence lifetime of the donor fluorophore. The fluorescence lifetime depends on the rate of energy transfer and hence decreases as the donor and acceptor come closer together. The distances between fluorescence labels attached to a molecule fluctuate due to conformational dynamics on a wide range of time scales. Extracting information about the dynamics is particularly challenging when the fluctuations are as fast as the time between photons. Our ability to study fast molecular dynamics is limited by the number of photons detected per unit time (photon count rate), which is proportional to the illumination intensity. To improve the dynamic range of single-molecule fluorescence spectroscopy, we consider each and every photon and use a maximum likelihood method to get the information about fast conformational dynamics. During this reporting period, we developed new methods of analyses of single-molecule experiments in collaboration with Dr. H.S. Chung from LCP (reference 1). The utility of these methods that include delay times has been demonstrated on several fast-folding proteins. By constructing two-dimensional FRET efficiency and lifetime histograms at various bin times, one can show the presence of the sub-microsecond to millisecond interdye distance fluctuations. We extended the previously developed theory to include delay times of photons emitted by the acceptor label. In order to determine the kinetics and lifetime parameters accurately, we used a more powerful maximum likelihood method adapted to include lifetime information. We found that the results of analyses that include donor delay times is very sensitive to fast acceptor blinking. Various strategies of taking acceptor blinking into account have been proposed. In single molecule force spectroscopy the response of an individual molecule to applied forces is probed using atomic force microscopes and laser tweezers. In these experiments, a biomolecule is attached, for example, to a mesoscopic (approximately micron size) bead that is trapped in the focus of a laser, via a long intervening polymer. To interpret such experiments, one must know the extent that the measured data reflect the behavior of the molecule of interest rather than the apparatus. In reference 2 we have developed an analytically tractable theory that can be used to determine the influence of the pulling device (apparatus) on the measured quantities, such as the rates of conformational changes. Consider a small biomolecule that is attached to a soft polymer linker that is pulled with a relatively large bead or cantilever. At constant force, the total extension stochastically changes between two (or more) values, indicating that the biomolecule undergoes transitions between two (or several) conformational states. Our goal was to determine the influence of the dynamics of the linker and mesoscopic pulling device on the force-dependent rate of the conformational transition extracted from the time dependence of the total extension, and the distribution of rupture forces in force-clamp and force-ramp experiments. For these different experiments, we derive analytic expressions for the observables that account for the mechanical response and dynamics of the pulling device and linker. Possible artifacts arise when the characteristic times of the pulling device and linker become comparable to, or slower than, the lifetimes of the metastable conformational states. We also revisit the problem of relating force-clamp and force-ramp experiments, and identify a linker and loading rate-dependent correction to the rates extracted from the latter. This work provides a framework for both the design and the quantitative analysis of force spectroscopy experiments by highlighting, and correcting for, factors that complicate their interpretation. It should be emphasized that the underlying theory required for us to be able to correct for artifacts in single molecule force experiments was developed in our seemingly esoteric paper, described in last year report, dealing with multidimensional reaction rate theory in the presence of anisotropic diffusion. This seems to us to be an excellent example of the fruitful interplay between pure and applied research. Another direction of our research is understanding the effect of diffusion on various biomolecular processes, including enzymatic modification of a multisite protein and stochastic gating. In the reversible stochastic gating (reference 3) a ligand can bind reversibly to a macromolecule when either can fluctuate between reactive and unreactive conformations. In these cases, the influence of the relative diffusive motion of the reactants cannot be described by simply altering the rate constants in the rate equations of chemical kinetics. An approximate but accurate theory is developed to describe the kinetics of the stochastic gating. The theory is based on a set of reaction-diffusion equations for the deviations of the pair distributions from their bulk values. The concentrations are shown to satisfy non-Markovian rate equations with memory kernels that are obtained by solving an irreversible geminate problem. The relaxation to equilibrium is not exponential but rather a power law. The concentration of molecules in cells can be so high that close to a half of the available space is occupied. Consequently the relative motion and interaction between molecules can be quite different in vivo from in vitro. In reference 4, we derive an analytical expression for the rate constant of a diffusion-influenced bimolecular reaction in a crowded environment that accounts for: (1) the slowdown of diffusion due to crowding and the dependence of the diffusivity on the distance between the reactants, (2) a crowding induced attractive short-range potential of mean force, and (3) nonspecific reversible binding to the crowders. This expression spans the range from reaction to diffusion control. Crowding can increase the reaction-controlled rate by inducing an effective attraction between reactants but decrease the diffusion-controlled rate by reducing their relative diffusivity. Consequently, the mechanism of ligand binding or protein-protein association can change from reaction controlled in vitro to diffusion-controlled in vivo.